Neutrinos have mass. Therefore, they can vary in speed. It is hard to measure speed exactly, but they travel very close to c. Higgs field model presumably covers their mass as well as for anything else.

In the Standard Model, the neutrino can gain a mass from the Higgs field just as the other particles do. However with just this, it is difficult to explain why their masses are so small. A better idea is to give them a Majorana mass term, which naturally leads to small nuetrino masses via the see-saw mechnism.